How do I get my screencast keys to stay by my world axes when I open & close my Tools panel?
I was slightely confused by your question, since you didnt mention that you are using non-default settings. 

Easy solution:

Disable "Region Overlap" in "User Preferences - System"



Fix:

If you want to use "Region Overlap" here is a small hackish patch to space_view3d_screencast_keys.py that should roughly do what you want:

def getDisplayLocation(context):
    scene   = context.scene
    mouse_size = scene.screencast_keys_mouse_size

    tool = context.area.regions[1] #coughs.. we just assume its there
    w = 0
    if bpy.context.user_preferences.system.use_region_overlap:
        w = tool.width

    pos_x = int( (context.region.width  - mouse_size * MOUSE_RATIO) * \
        scene.screencast_keys_pos_x / 100 + w)
    pos_y = int( (context.region.height - mouse_size) *
        scene.screencast_keys_pos_y / 100)

    return(pos_x, pos_y)


Whole file is here: space_view3d_screencast_keys.py

Just find your scripts/addons folder, move the old file and place this one there.

Slightly safer might be to query for the tools panel but it comes with some overhead:

w = 0
for region in context.area.regions:
    if region.type == 'TOOLS' and bpy.context.user_preferences.system.use_region_overlap:        
        w = region.width
        break